Numerical puzzles such as SUDOKU or FUTOSHIKI may be solved by placing numerical values in empty regions of the puzzle, so that each region is filled in a manner that is consistent with any provided clues and pre-filled values in the puzzle, and conformant to the puzzle's logical rules. Such puzzles are not mathematical puzzles in that they do not require any mathematical problems to be solved to complete the puzzles. Whether numerical or mathematical, such puzzles may be embodied on printed mediums such as paper or other manufactured objects, or in computer programs that allow users to play the puzzle. Issues faced by the producers of such puzzles may involve generating new puzzles. For some types of mathematical puzzles, it may be difficult or impossible to generate puzzles without resorting to computer-based techniques.